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摘要翻译：
考虑一个理想的$I\子集R=\bc[x_1,...,x_n]$定义了一个复杂的仿射变量$X\子集\bc^n$。我们用{\em数值主分解}(NPD)来描述与$I$相关联的分量。该方法是基于在高维复杂空间中定义{em defresed variety}$DXD$的{em defresed variety}$I^{(d)}$的构造。对于每个嵌入的组件，都存在$d$和一个独立的组件$\dyd$$$\did$投射到$y$上。反过来，$\dyd$可以通过现有的素分解方法来发现，特别是应用于$\dxd$的{\em数值不可约分解}。NPD的概念通过用{\em见证集}表示每个组件，给出了方案$\spec(R/I)$的完整描述。我们提出了一个算法来产生一个包含NPD的见证集集合，该集合可以用来解决$I$的{\em理想隶属度问题}。
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英文标题：
《Numerical primary decomposition》
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作者：
Anton Leykin
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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英文摘要：
Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine variety $X \subset \bC^n$. We describe the components associated to $I$ by means of {\em numerical primary decomposition} (NPD). The method is based on the construction of {\em deflation ideal} $I^{(d)}$ that defines the {\em deflated variety} $\dXd$ in a complex space of higher dimension. For every embedded component there exists $d$ and an isolated component $\dYd$ of $\dId$ projecting onto $Y$. In turn, $\dYd$ can be discovered by existing methods for prime decomposition, in particular, the {\em numerical irreducible decomposition}, applied to $\dXd$. The concept of NPD gives a full description of the scheme $\Spec(R/I)$ by representing each component with a {\em witness set}. We propose an algorithm to produce a collection of witness sets that contains a NPD and that can be used to solve the {\em ideal membership problem} for $I$.
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PDF链接：
https://arxiv.org/pdf/0801.3105
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